Effects of quenching protocols based on parametric oscillators

TL;DR

This paper analyzes quantum parametric oscillators with time-dependent frequencies modeled by Morse potentials, deriving solutions for their dynamics and exploring quantum state evolution and uncertainty relations under various quenching protocols.

Contribution

It provides a closed-form solution for the amplitude of quasi-normal modes in quantum parametric oscillators with Morse-like frequency variations, offering new insights into their dynamical behavior.

Findings

Derived explicit solutions for quasi-normal mode amplitudes.

Analyzed quantum state evolution and uncertainty principles.

Identified key features of dynamics under different quenching protocols.

Abstract

We consider the problem of understanding the basic features displayed by quantum systems described by parametric oscillators whose time-dependent frequency parameter $\omega(t)$ varies continuously during evolution so to realise quenching protocols of different types. To this scope we focus on the case where $\omega(t)^2$ behaves like a Morse potential, up to possible sign reversion and translations in the $(t,\omega^2)$ plane. We derive closed form solution for the time-dependent amplitude of quasi-normal modes, which is the very fundamental dynamical object entering the description of both classical and quantum parametric oscillators, and highlight its significant characteristics for distinctive cases arising based on the driving specifics. After doing so, we provide an insight on the way quantum states evolve by paying attention on the position-momentum Heisenberg uncertainty principle and the statistical aspects implied by second-order correlation functions over number-type states.